P-release kinetic as a predictor for P-availability in the STYCS Trials
In my Internship I studied the current GRUD, particularly Mg, P and K
Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)
Currently only stationary measurement of STP are considered
Could a kinetic desorption-model better explain the soil status and yield data?
The net-desorption was modeled using a first-order kinetic equation:
1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]
2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]
We compared two approaches to predict agronomic outcomes:
The Standard Method
These are static “snapshots” of the soil’s P capacity.
The Kinetic Method
This approach measures P as a dynamic process.
We tested the models against three agronomic metrics:
1. Normalized Yield (\(Y_{norm}\)) - How well did the crop perform relative to its maximum potential at that specific site?
2. P-Export (\(P_{up}\)) - How much phosphorus did the crop remove from the field?
3. P-Balance (\(P_{bal}\)) - What is the long-term surplus or deficit of P in the soil? This is a key indicator of sustainability.
To ensure a fair and robust comparison, we used a consistent statistical approach:
1. Linear Mixed-Effects Models (lmer) - We built a separate model for each agronomic outcome (Yield, P-Export, P-Balance). - This approach accounts for the nested structure of the STYCS experiment (sites, years, blocks).
2. Standardized Coefficients (β) - All numeric variables were scaled and centered (mean=0, sd=1). - This allows us to directly compare the effect size of each predictor. A larger coefficient means a stronger effect.
3. The Comparison - In the following tables, each column represents a separate model where we test a different set of predictors.
A robust P metric should reflect both the soil’s inherent properties (like texture and pH) and the impact of management (fertilization). We modeled each metric to see what drives it.
| Model | PS | k | J0 | P-CO2 | P-AAE10 |
|---|---|---|---|---|---|
| Alox | 0.136 | -0.660 | -1.204 | -0.034 | -0.319 |
| Feox | -0.098 | 0.020 | -0.571 | -0.164 | -0.138 |
| Clay | -0.062 | -1.733** | 0.611 | -0.007 | -0.121 |
| C-org | 0.351* | 1.044** | -0.412 | 0.166 | 0.232 |
| pH | -0.058 | -0.280 | 0.094 | 0.075 | 0.057 |
| Silt | -0.046 | 0.252 | 0.113 | -0.084 | 0.012 |
| marginal R² | 0.175 | 0.204 | 0.224 | 0.125 | 0.280 |
| conditional R² | 0.894 | 0.963 | 0.976 | 0.724 | 0.832 |
First, we tested which P metric was best at predicting site-normalized yield (\(Y_{norm}\)).
| Model | P-CO2 only | P-AAE10 only | GRUD Model | Kinetic Model |
|---|---|---|---|---|
| k | 0.166 | |||
| J0 | -0.012 | |||
| PS | 0.066 | |||
| P-AAE10 | 0.067* | 0.432** | ||
| P-CO2 | 0.027 | -0.128 | ||
| P-CO2 * P-AAE10 | 0.149* | |||
| marginal R² | 0.012 | 0.084 | 0.291 | 0.019 |
| conditional R² | 0.083 | 0.361 | 0.436 | 0.045 |
| Model | P-CO2 only | P-AAE10 only | GRUD Model | Kinetic Model |
|---|---|---|---|---|
| k | -0.014 | |||
| J0 | 0.080 | |||
| PS | -0.018 | |||
| P-AAE10 | 0.025 | -0.015 | ||
| P-CO2 | 0.087 | 0.131 | ||
| P-CO2 * P-AAE10 | 0.011 | |||
| marginal R² | 0.012 | 0.001 | 0.016 | 0.004 |
| conditional R² | 0.654 | 0.685 | 0.796 | 0.789 |
Observation: Here, the results are less clear. P-Export is a more complex variable to predict, and no single model or predictor stands out as being consistently powerful. ## P-balance model summary:
| Model | P-CO2 only | P-AAE10 only | GRUD Model | Kinetic Model |
|---|---|---|---|---|
| k | 0.155 | |||
| J0 | -0.151 | |||
| PS | 0.341*** | |||
| P-AAE10 | 0.009 | 0.009 | ||
| P-CO2 | -0.023 | -0.029 | ||
| P-CO2 * P-AAE10 | 0.030 | |||
| marginal R² | 0.001 | 0.000 | 0.006 | 0.122 |
| conditional R² | 0.590 | 0.762 | 0.596 | 0.699 |
PS (the P pool) was vastly superior, while standard tests showed no predictive power.My research concludes that the ideal soil P test depends on the question being asked:
For Routine Fertilization
To answer a farmer’s question: “Is P limiting my yield this year?”
The Standard Soil Tests are effective and well-suited.
For Long-Term Sustainability
To answer a policymaker’s question: “Is this soil’s P status sustainable?”
A Kinetic Approach is the superior and necessary tool.